Chapter 3 Solutions. Answers to Concepts Review and Critical Thinking Questions

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1 Answers to Concepts Review and Critical Thinking Questions 1. a. If inventory is purchased with cash, then there is no change in the current ratio. If inventory is purchased on credit, then there is a decrease in the current ratio if it was initially greater than 1.0. b. Reducing accounts payable with cash increases the current ratio if it was initially greater than 1.0. c. Reducing short-term debt with cash increases the current ratio if it was initially greater than 1.0. d. As long-term debt approaches maturity, the principal repayment and the remaining interest expense become current liabilities. Thus, if debt is paid off with cash, the current ratio increases if it was initially greater than 1.0. If the debt has not yet become a current liability, then paying it off will reduce the current ratio since current liabilities are not affected. e. Reduction of accounts receivables and an increase in cash leaves the current ratio unchanged. f. Inventory sold at cost reduces inventory and raises cash, so the current ratio is unchanged. g. Inventory sold for a profit raises cash in excess of the inventory recorded at cost, so the current ratio increases. 2. The firm has increased inventory relative to other current assets; therefore, assuming current liability levels remain mostly unchanged, liquidity has potentially decreased. 3. A current ratio of 0.50 means that the firm has twice as much in current liabilities as it does in current assets; the firm potentially has poor liquidity. If pressed by its short-term creditors and suppliers for immediate payment, the firm might have a difficult time meeting its obligations. A current ratio of 1.50 means the firm has 50% more current assets than it does current liabilities. This probably represents an improvement in liquidity; short-term obligations can generally be met completely with a safety factor built in. A current ratio of 15.0, however, might be excessive. Any excess funds sitting in current assets generally earn little or no return. These excess funds might be put to better use by investing in productive long-term assets or distributing the funds to shareholders. 4. a. Quick ratio provides a measure of the short-term liquidity of the firm, after removing the effects of inventory, generally the least liquid of the firm s current assets. b. Cash ratio represents the ability of the firm to completely pay off its current liabilities balance with its most liquid asset (cash). c. The capital intensity ratio tells us the dollar amount investment in assets needed to generate one dollar in sales. d. Total asset turnover measures how much in sales is generated by each dollar of firm assets. e. Equity multiplier represents the degree of leverage for an equity investor of the firm; it measures the dollar worth of firm assets each equity dollar has a claim to. f. Long-term debt ratio measures the percentage of total firm capitalization funded by long-term debt. g. Times interest earned ratio provides a relative measure of how well the firm s operating earnings can cover current interest obligations. h. Profit margin is the accounting measure of bottom-line profit per dollar of sales. i. Return on assets is a measure of bottom-line profit per dollar of total assets. j. Return on equity is a measure of bottom-line profit per dollar of equity. k. Price-earnings ratio reflects how much value per share the market places on a dollar of accounting earnings for a firm. 5. Common size financial statements express all balance sheet accounts as a percentage of total assets and all income statement accounts as a percentage of total sales. Using these percentage values rather than nominal dollar values facilitates comparisons between firms of different size or business type.

2 6. Peer group analysis involves comparing the financial ratios and operating performance of a particular firm to a set of peer group firms in the same industry or line of business. Comparing a firm to its peers allows the financial manager to evaluate whether some aspects of the firm s operations, finances, or investment activities are out of line with the norm, thereby providing some guidance on appropriate actions to take to adjust these ratios if appropriate. An aspirant group would be a set of firms whose performance the company in question would like to emulate. The financial manager often uses the financial ratios of aspirant groups as the target ratios for his or her firm; some managers are evaluated by how well they match the performance of an identified aspirant group. 7. Return on equity is probably the most important accounting ratio that measures the bottom-line performance of the firm with respect to the equity shareholders. The Du Pont identity emphasizes the role of a firm s profitability, asset utilization efficiency, and financial leverage in achieving a ROE figure. For example, a firm with ROE of 20% would seem to be doing well, but this figure may be misleading if it were a marginally profitable (low profit margin) and highly levered (high equity multiplier). If the firm s margins were to erode slightly, the ROE would be heavily impacted. 8. The book-to-bill ratio is intended to measure whether demand is growing or falling. It is closely followed because it is a barometer for the entire high-tech industry where levels of revenues and earnings have been relatively volatile. 9. If a company is growing by opening new stores, then presumably total revenues would be rising. Comparing total sales at two different points in time might misleading. Same-store sales control for this by only looking at revenues of stores open within a specific period. 10. a. For an electric utility such as Con Ed, expressing costs on a per kilowatt hour basis would be a way comparing costs with other utilities of different sizes. b. For a retailer such as Sears, expressing sales on a per square foot basis would be useful in comparing revenue production against other retailers. c. For an airline such as Delta, expressing costs on a per passenger mile basis allows for comparisons with other airlines by examining how much it costs to fly one passenger one mile. d. For an on-line service such as AOL, using a per call basis for costs would allow for comparisons with smaller services. A per subscriber basis would also make sense. e. For a hospital such as Holy Cross, revenues and costs expressed on a per bed basis would be useful. f. For a college textbook publisher such as McGraw-Hill/Irwin, the leading publisher of finance textbooks for the college market, the obvious standardization would be per book sold. Solutions to Questions and Problems Basic 1. NWC = $900 = CA CL; CA = $ ,320 = $5,220 Current ratio = CA / CL = $5,220 / $4,320 = 1.21 times Quick ratio = (CA Inventory) / CL = ($5,220 1,900) / $4,320 = 0.77 times 2. Profit margin = Net income / Sales; Net income = ($41M)(0.12) = $4.92 million ROA = Net income / TA = $4.92M / $32M = 15.38% ROE = Net income / TE = Net income / (TA TD) = $4.92M / ($32M 11M) = 23.43% 3. Receivables turnover = Sales / Receivables = $2,131,516 / $308,165 = 6.92 times

3 Days sales in receivables = 365 days / Receivables turnover = 365 / 6.92 = days The average collection period for an outstanding accounts receivable balance was days. 4. Inventory turnover = COGS / Inventory = $1,843,127 / $921,386 = 2.00 times Days sales in inventory = 365 days / Inventory turnover = 365 / 2.00 = days On average, a unit of inventory sat on the shelf days before it was sold. 5. Total debt ratio = 0.45 = TD / TA = TD / (TD + TE); 0.55(TD) = 0.45(TE) Debt-equity ratio = TD / TE = 0.45 / 0.55 = 0.82 Equity multiplier = 1 + D/E = NI = Addition to retained earnings + Dividends = $300K + 220K = $520K EPS = NI / Shares = $520K / 300K = $1.73 per share DPS = Dividends / Shares = $220K / 300K = $0.73 per share BVPS = TE / Shares = $5M / 300K = $16.67 per share Market-to-book ratio = Share price / BVPS = $25 / $16.67 = 1.50 times P/E ratio = Share price / EPS = $25 / $1.73 = times 7. ROE = (PM)(TAT)(EM) = (.11)(1.05)(1.60) = 18.48% 8. ROE =.1720 = (.12)(1.35)(EM); EM = 1.062; D/E = EM 1 = Payables turnover = COGS / Payables = $18,364 / $3,105 = 5.91 times Days sales in payables = 365 days / Payables turnover = 365 / 5.91 = days The company left its bills to suppliers outstanding for days on average. A large value for this ratio could imply that either (1) the company is having liquidity problems, making it difficult to pay off its short-term obligations, or (2) that the company has successfully negotiated lenient credit terms from its suppliers. 10. EM = 1 + D/E = 1.80 ROE = (ROA)(EM) =.084(1.80) = 15.12% ROE = NI / TE; NI = (.1512)($430,000) = $65,016

4 11. b = 1.30 =.70; internal g = [.19(.70) ] / [1.19(.70)] = 15.34% 12. b = 1.40 =.60; sustainable g = [.17(.60)] / [1.17(.60)] = 11.36% 13. ROE = (PM)(TAT)(EM) = (.102)(1/.70)(1 +.50) = 21.86% b = 1 ($6,000 / $30,000) =.80; sustainable g = [.2186(.80) ] / [1.2186(.80)] = 21.19% 14. ROE = (PM)(TAT)(EM) = (.065)(1.90)(2.05) = 25.32% b = 1.30 =.70; sustainable g = [.2532(.70)] / [1.2532(.70)] = 21.54% # #15 Assets Current assets Cash $ 16, % $ 19, % Accounts receivable 48, % 52, % Inventory 100, % 137, % Total $165, % $209, % Fixed assets Net plant and equipment 537, % 535, % Total assets $702, % $744, % Liabilities and Owners Equity Current liabilities Accounts payable $161, % $137, % Notes payable 74, % 96, % Total $236, % $234, % Long-term debt 150, % 125, % Owners equity Common stock and paid-in surplus $150, % $150, % Accumulated retained earnings 166, % 235, % Total $316, % $385, % Total liabilities and owners equity $702, % $744, % 16. a. CR02 = $165,271 / $236,101 = 0.70; CR03 = $209,747 / $234,148 = 0.90 b. QR02 = ($165, ,387) / $236,101 = 0.27 QR03 = ($209, ,806) / $234,108 = 0.31 c. Cash ratio02 = $16,150 / $236,101 = 0.07; Cash ratio03 = $19,125 / $234,148 = 0.08 d. D/E02 = ($236, ,000) / $316,861 = 1.22 EM02 = 1 + D/E99 = 2.22 D/E03 =($234, ,000) / $385,826 = 0.93 EM03 = 1 + D/E00 = 1.93 e. TDR02 = ($236, ,000) / $702,962 = 0.55 TDR03 = ($234, ,000) / $744,974 = ROE = ($157,320 / $1,986,382)($1,986,382 / $744,974)($744,974 / $385,826) = 40.77%

5 18. ROA = Profit margin Total asset turnover; Total asset turnover =.11 /.09 = 1.22 ROE = ROA Equity multiplier Equity multiplier =.24 /.11 = PM = NI / sales; NI = (.13)($22,000,000) = $2,860,000 ROA = NI / TA = $2,860,000 / $22,500,000 = 12.71% 20. ROA = NI / TA = $11,071 / $68,000 =.1628 b = 1.40 =.60 internal g = [(.1628)(.60)] / [1 (.1628)(.60)] = 10.83% 21. ROE = NI / E = $11,071 / $23,000 =.4814 b = 1.40 =.60 sustainable g = [(.4814)(.60)] / [1 (.4814)(.60)] = 40.61% 22. TAT = Sales / TA = $15M / $8M = times Sales = TA TAT = $8M 2.25 = $18M 23. Debt ratio = (TA E) / TA =.70 = $140,000 / TA; TA = $200,000 Equity = $200, ,000 = $60,000 ROE = NI / Equity = $14,000 / 60,000 = EPS = NI / Shares = $6,100,000 / 3,400,000 = $1.79 PE = Price / EPS = $70 / $1.79 = Book value per share = Book value of equity / Shares = $31M / 3.4M = $9.12 per share Market-to-book = Market value per share / Book value per share = $70 / $9.12 = TAT = Sales / TA = 2.9 = Sales / $8M; Sales = $23.2M ROA = NI / TA =.11 = NI / $8M; NI = $880,000 PM = NI / Sales = $880,000 / $23.2M = 3.79% Intermediate 26. ROE = 0.12 = (PM)(TAT)(EM) = (PM)(S / TA)(1 + D/E) PM = [(0.12)($800)] / [(1 + 1)($3,680)] =.013 PM =.013 = NI / S; NI =.013($3,680) = $ CR = 1.20 = CA / CL; CA = 1.20($750) = $ PM =.09 = NI / sales; NI =.09($3,920) = $ ROE =.185 = NI / TE; TE = $ /.185 = $1, Long-term debt ratio = 0.65 = LTD / ( LTD + TE ) 1 + TE / LTD = 1.538; LTD = $1, /.538 = $3, TD = CL + LTD = $750 + $3, = $4, TA = TD + TE = $4, $1, = $6, NFA = TA CA = $6, = $5,298.65

6 28. Child: profit = $0.50 / $25 = 2%; store: profit margin = NI / S = $4.5 / $450M = 1% The advertisement is referring to the store s profit margin, but a more appropriate earnings measure for the firm s owners is the return on equity. ROE = NI / TE = NI / (TA TD) = $4.5M / ($105.0M 67.5M) = 12.00% 29. Days sales in receivables = days = 365 days / Receivables turnover Receivables turnover = Sales / Days sales in receivables Sales = ($138,600)(365) / = $2,352, PM = NI / S = $141,200 / $2,352, = 6.00% TAT = S / TA = $2,352, / $960,000 = 2.45 times EM = 1 + D/E = 2.15 ROE = (PM)(TAT)(EM) = (.0600)(2.45)(2.15) = 31.62% 30. Net income = (1 t)ebt; EBT = $6,820 / 0.66 = $10, EBIT = EBT + Interest paid = $10, ,931 = $12, Cash coverage ratio = (EBIT + Depreciation expense) / Interest Cash coverage ratio = ($12, ,380 ) / $1,931 = 7.07 times 31. Sales COGS Dep. = EBIT = $380K 93K 47K = $240K DPS = Dividends / Shares; Dividends = $1.70(20,000) = $34K Net income = Dividends + Additions to retained earnings = $34, ,420 = $95,420 EBT = NI / (1 t) = $95,420 / 0.66 = $144, EBIT EBT = Interest paid = $240,000 $144, = $95, Times interest earned ratio = EBIT / interest = $240,000 / $95, = 2.52 times 32. Total debt ratio = TD / TA =.40 = $300K / TA; TA = $300K /.40 = $750K TA = TD + E = $750K = $300K + E; E = $450K ROE = NI / E =.15 = NI / $450K; NI = (.15)($450K) = $67,500 ROA = NI / TA = $67,500 / $750K = 9.00% 33. PM = NI / S = 10,386 / 161,583 = 6.43% As long as both net income and sales are measured in the same currency, there is no problem; in fact, except for some market value ratios like EPS and BVPS, none of the financial ratios discussed in the text are measured in terms of currency. This is one reason why financial ratio analysis is widely used in international finance to compare the business operations of firms and/or divisions across national economic borders. NI = ($362,814) = $23, Short-term solvency ratios: CR02 = $10,210 / $3,014 = 3.39 times CR03 = $12,700 / $3,050 = 4.16 times QR02 = ($10,210 6,218) / $3,014 = 1.32 times QR03 = ($12,700 6,462) / $3,050 = 2.05 times Cash ratio02 = $1,180 / $3,014 = 0.39 times Cash ratio03 = $2,122 / $3,050 = 0.70 times

7 Asset utilization ratios: TAT = $26,800 / $36,516 = 0.73 times Inventory turnover = $8,400 / $6,462 = 1.30 times Receivables turnover = $26,800 / $4,116 = 6.51 times Long-term solvency ratios: Total debt ratio02 = ($3, ,815) / $33,582 = 0.38 Total debt ratio03 = ($3, ,518) / $36,516 = 0.37 D/E02 = ($3, ,815) / $20,753 = 0.62 D/E03 = ($3, ,518) / $22,984 = 0.59 EM02 = 1 + D/E02 = 1.62; EM03 = 1 + D/E03 = 1.59 TIE ratio = $17,000 / $1,250 = times Cash coverage ratio = ($17, ,400) / $1,250 = times Profitability ratios: PM = $10,395 / $26,800 = 38.79% ROA = $10,395 / $36,516 = 28.47% ROE = $10,395 / $22,948 = 45.30% 35. ROE = (NI / Sales)(Sales / TA)(TA / E) = ($10,395 / $26,800)($26,800 / $36,516)($36,516 / $22,948) = EPS = $10,395 / 10,000 shares = $ per share P/E ratio = $24 / $ = times DPS = $8,200 / 10,000 shares = $0.82 per share BVPS = $22,948 / 10,000 shares = $ per share Market-to-book ratio = $24.00 / $ = times 37. The current ratio appears to be relatively high when compared to the median, however it is below the upper quartile, meaning that at least 25 percent of firms in the industry have a higher current ratio. Overall, it does not appear that the current ratio is out of line with the industry. The total asset turnover is low when compared to the industry. In fact, the total asset turnover is in the lower quartile. This means that the company does not use assets as efficiently overall or that the company has newer assets than the industry. This would mean that the assets have not been depreciated, which would mean a higher book value and a lower total asset turnover. The debt-equity ratio is in line with the industry, between the mean and the upper quartile. The profit margin is approximately three times as large as the industry median and over twice as large as the upper quartile, which is exceptional. The company may be better at controlling costs, or has a better product which enables them to charge a premium price. 38. b = 1.40 =.60; sustainable g =.08 = [ROE(.60)] / [1 ROE(.60)]; ROE = 12.35% ROE =.1235 = PM(1 / 1.50)(1 +.55); PM = (.1235)(1.50) / 1.55 = 11.95% 39. b = 1.30 =.70; sustainable g =.09 = [ROE(.70 )] / [1 ROE(.70)]; ROE = 11.80% ROE =.1180 = (.07)(1 /.8)EM; EM = (.1180)(.8) /.07 = 1.35; D/E = b = 1.70 =.30; internal g =.06 = [ROA(.30)] / [1 ROA(.30)]; ROA =.1887 ROA =.1887 = (PM)(TAT); TAT =.1887 /.11 = 1.715

8 41. TDR = 0.60 = TD / TA; 1 / 0.60 = TA / TD = 1 + TE / TD; D/E = 1 / [(1 / 0.60) 1] = 1.5 ROE = (PM)(TAT)(EM) = (.085)(1.50)( ) = ROA = (PM)(TAT) =.085(1.50) = 12.75%; b = 1.40 =.60; sustainable g = [.31875(.60)] / [ (.60)] = 23.65% 42. b = 1 ($2,100 / $7,000) =.30; ROE = NI / TE = $7,000 / $24,000 = 29.17% sustainable g = [.70(.2917)] / [1.70(.2917)] = 25.65% new TA = ($75,000) = $94, new TD = [D / (D + E)](TA) = (51/75)($94,240.84) = $64, additional borrowing = $64, $51,000 = $13, ROA = NI / TA = $7,000 / $75,000 =.0933; internal g = [.0933(.70)] / [1.0933(.70)] = 6.99% 43. ROE = (PM)(TAT)(EM) = (.08)(0.95)( ) = 9.88% sustainable g =.13 = [.0988(b)] / [1.0988(b)]; b = 1.16; payout ratio = 1 b =.16 This is a negative dividend payout ratio of 116%, which is impossible; the growth rate is not consistent with the other constraints. The lowest possible payout rate is 0, which corresponds to b = 1, or total earnings retention. max sustainable g =.0988 / (1.0988) = 10.96%